Convergent Interval Confirmation for Three‐Step Discrete Specific Zeroing Neural Dynamics Illustrated With Repetitive Motion Planning of Redundant Manipulators

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ABSTRACT Repetitive motion planning (RMP) for redundant manipulators with high convergent precision becomes an intense research topic due to its more degrees of freedom. In this paper, a specific zeroing neural dynamics (SZND) model for the RMP is first set up via zeroing neurodynamics. After that, a general linear three‐step rule is presented and applied to discretise the SZND model. Then, we obtain a three‐step discrete SZND (TS‐DSZND) model for repetitive kinematics. It is necessary to point out that the stepsize in TS‐DSZND algorithm is intimated to the stability of the proposed TS‐DSZND. By utilizing linear transformation and the Jury stability criterion, the optimal stepsize interval of the TS‐DSZND is obtained by a theorem. Furthermore, the truncation error constant, which tends to be neglected with most of the ZeaD‐typed discretisation formulas for the RMP of redundant manipulators, is analysed and exhibits the impact for the convergent accuracy compared with the corresponding three‐step rules. Besides, simulative illustrations on various redundant manipulators show the superiority and feasibility of the proposed TS‐DSZND as well as the effective stepsize domain. Finally, a physical experiment on a real UR5 robotic arm for fulfiling a flower‐shaped path validates the satisfying performance of the TS‐DSZND model.

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